Question 1107481: a) The perimeters of two similar triangles are 110 and 65. If the altitude of the smaller triangle is 5, how long is the corresponding altitude of the other triangle?
b) One of two similar triangles has an area 1/4 times that of the other. What is the ratio of the perimeters of the triangle?
Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113)   (Show Source):
You can put this solution on YOUR website! a) 65/110 = 5/x
x = (65 * 5)/110 = 2.954
b) Without loss of generality, let the side lengths of the triangles be (3, 4, 5) and (6, 8, 10).
The ratio of perimeters is  = 1/2
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
a) perimeter and altitude are both linear measurements, so the ratio of the altitudes is the same as the ratio of the perimeters.
The ratio of similarity is 110:65 = 22:13; the altitude of the larger triangle is 5*(22/13) = 110/13.
ANSWER: 110/13
b) Area is a measurement in two dimensions; perimeter is a measurement in one dimension. For ANY two similar figures, if the ratio of linear measurements is a:b then the ratio of corresponding area measurements is a^2:b^2.
Given that the ratio of areas of two similar triangles is 1:4, we know that the ratio of any linear measurements between the two figures is 1:2.
ANSWER: 1:2
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